the icons, no
the apps they represent, yes, but minimal. I wouldn't worry about them. Now other programs in the systray can use more resources ( depending on what the app). to check, check your resources,

Maybe the network icon
But it takes not so much memory.
Right click the icon and change the settings so it disappears.
Or go To Start / Settings / Control Panel and open the icon coming with your network card

the icons, no
the apps they represent, yes, but minimal. I wouldn't worry about them. Now other programs in the systray can use more resources ( depending on what the app). to check, check your resources, and then end task on the app, and check the resources again

Anything you see on the screen uses some memory and in the case of the icons in the tray they use very little that it is really unlikely to have any affect on the system what so ever. Even if you hide the icons the icons and the applications they represent are still resident in memory. If you want to hide them so there is more room on task bar then this can be accomplished through a third party utility like this free one at ZDNET

Description:
TrayManager lets you control the explosion of icons in your system tray by creating a submenu for the icons you use less frequently. The original TrayManager worked only under Windows 95 and Windows 98. Version 2.0 adds support for Windows ME, Windows NT 4, and Windows 2000. A new feature restores the icons in your system tray after an Explorer crash. A simple configuration window lets you choose which icons to place on the TrayManager submenu. Double-click on TrayManager's tray icon to bring up the configuration dialog. Place the icons you use less often into a submenu to make it quicker and easier to find the ones you frequently need. To access the icons in the submenu, right-click on TrayManager's tray icon, and then select the item you want from the list. Right- and left-clicks on a submenu item work just as if the item were still in the system tray. TrayManager was written by Steven E. Sipe, and first appeared in PC Magazine November 21, 2000 (v19n20). Source code is included.

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